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There is no one private key associated with the 12 word mnemonic that you posses. Consider the seed phrase to be like a keychain, that holds multiple keys. You would need to import the 12 word mnemonic you possess into a wallet software in order to generate the private keys. The wallet software will then scan the Bitcoin blockchain in order to see the funds that those keys control. A use of a hardware wallet is most recommended in order to ensure the privacy of these keys.

Care should however, to use the same derivation path for the keys that was used when you generated the addresses to receive the funds. This can be looked up based on what wallet software you used while generating the 12 word mnemonic. There are multiple derivation paths that wallets use. Some use BIP 44 while others use BIP 49 or even BIP 84.